package euler.p051_100;

import euler.MainEuler;

public class Euler073 extends MainEuler {

    /*
        Consider the fraction, n/d, where n and d are positive integers.
        If n<d and HCF(n,d)=1, it is called a reduced proper fraction.

        If we list the set of reduced proper fractions
        for d ≤ 8 in ascending order of size, we get:

        1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7,
        1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

        It can be seen that there are 3 fractions between 1/3 and 1/2.

        How many fractions lie between 1/3 and 1/2 in the sorted
        set of reduced proper fractions for d ≤ 12,000?

        Note: The upper limit has been changed recently.
     */
    public String resolve() {

        int limite = 12000;
        int count = 0;

        for (int denum = 1; denum <= limite; denum++) {
            for (int num = denum/3 + 1; 2*num < denum; num++) {
                if (primeHelper.relativelyPrimes(denum, num)) {
                    count++;
                }
            }
        }

        return String.valueOf(count);
        // 7295372
    }

}
